Problem: Solve for $c$: \[\frac{c-23}{2} = \frac{2c +5}{7}.\]
Solution: Multiplying both sides by 2 and by 7 to eliminate fractions gives  \[7(c-23) = 2(2c+5).\] Expanding both sides gives $7c - 161 = 4c + 10$.  Subtracting $4c$ from both sides gives $3c -161= 10$, and adding 161 to both sides gives $3c = 171$.  Finally, dividing by 3 gives $c = \frac{171}{3} = \boxed{57}$.